Recent activity
New submissions and commentary edits, newest first.
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commented on curve #245
Rank-20 at naive height 207.89: Mestre-family specialization T=5801/160 found by wide-denominator vectorized sieve (n>20 window), certified via famcert3 with base-point injection. -
submitted curve #245 — rank ≥ 20, naive height 207.89
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commented on curve #244
Found by Noam D. Elkies in June 2026, using an improved version of the methods described in his JMM 2023 talk https://abel.math.harvard.edu/~elkies/Elkies_JMM23.pdf -
submitted curve #244 — rank ≥ 14, naive height 85.19
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commented on curve #41
Found by Brumer - McGuinness. A rank 5 example from their elliptic-curve examples page, with independent points of x-coordinates 5, 4, 3, 7, 0. This curve has rank exactly 5 (verified by both mwrank and the gp function ellrank(). -
commented on curve #243
New curve of rank >= 20 and naive height 218.2916, beating the previous rank-20 record 223.3165 (#92). Found as the specialization T = 3895/6 of the Mestre/Fermigier rank-12 quartic family on the rational Mestre sextuple mestre_ais(u = -7/2, v = 3/2) (roots {-1455/4, 2955/4, 1437… -
submitted curve #243 — rank ≥ 20, naive height 218.29
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commented on curve #242
Rank >= 18 via 18 independent rational points with a positive-definite Neron-Tate height-pairing matrix. Mestre/Fermigier u4_v6 family, T=4694. Independently cross-verified in Sage and Magma; finite-field product independence backstop. Lower bound only; no exact-rank or upper-bou… -
submitted curve #242 — rank ≥ 18, naive height 194.67
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commented on curve #241
Generated by rational Mestre (u,v) discriminant search: u=-1/2, v=7/2, T=429/2; exact abs-discriminant frontier triage. -
submitted curve #241 — rank ≥ 18, naive height 159.97
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commented on curve #240
Generated by rational Mestre (u,v) discriminant search: u=-3, v=-1/2, T=2229/16; exact abs-discriminant frontier triage. -
submitted curve #240 — rank ≥ 19, naive height 166.83
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commented on curve #239
Rank ≥15. Mestre construction from the rational 6-tuple family a(u,v)={u,v,-u-v,-u(u+2v)²/((u-v)(2u+v)),v(2u+v)²/((u-v)(u+2v)),(u-v)²(u+v)/((u+2v)(2u+v))} at (u,v)=(1,-3), cleared tuple [20, -60, 40, 125, 3, -128], shift t=213. Two depressed cubics with equal product (satisfies M… -
submitted curve #239 — rank ≥ 15, naive height 145.27
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commented on curve #238
Rank ≥15. Mestre construction from the rational 6-tuple family a(u,v)={u,v,-u-v,-u(u+2v)²/((u-v)(2u+v)),v(2u+v)²/((u-v)(u+2v)),(u-v)²(u+v)/((u+2v)(2u+v))} at (u,v)=(-7,-1), cleared tuple [-210, -30, 240, 189, -125, -64], shift t=1791/4. This family satisfies the Mestre S=0 degree… -
submitted curve #238 — rank ≥ 15, naive height 166.41
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commented on curve #237
Rank ≥15. Mestre construction from the rational 6-tuple family a(u,v)={u,v,-u-v,-u(u+2v)²/((u-v)(2u+v)),v(2u+v)²/((u-v)(u+2v)),(u-v)²(u+v)/((u+2v)(2u+v))} at (u,v)=(-10,-1), cleared tuple [-840, -84, 924, 640, -343, -297], shift t=784/1. This family satisfies the Mestre S=0 degre… -
submitted curve #237 — rank ≥ 15, naive height 137.68
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commented on curve #236
Rank ≥16. Mestre construction from the rational 6-tuple family a(u,v)={u,v,-u-v,-u(u+2v)²/((u-v)(2u+v)),v(2u+v)²/((u-v)(u+2v)),(u-v)²(u+v)/((u+2v)(2u+v))} at (u,v)=(-7,-4), cleared tuple [-210, -120, 330, 875, -864, -11], shift t=606/1. This family satisfies the Mestre S=0 degree… -
submitted curve #236 — rank ≥ 16, naive height 167.76
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commented on curve #234
Rank-19 height AND conductor record: h=180.457 (beats 190.312), log N=142.954 (beats 146.224). New 3-parameter sub-family of Mestre locus 12*p5=5*p2*p3: six roots = union of two depth-2 cubics x^3+px+q, x^3+rx+s with (p-r)(q-s)=0 (equal product), disjoint from Mestre (u,v) slice.… -
commented on curve #235
Rank-15 naive-height record: h=120.642 (beats 127.132). New 3-parameter sub-family of Mestre locus 12*p5=5*p2*p3: six roots = union of two depth-2 cubics with (p-r)(q-s)=0 (equal product), beyond Mestre (u,v) slice. Sextuple {0,7,133,136,430,434}, T=162; base-point injection + Ne… -
submitted curve #235 — rank ≥ 15, naive height 120.64
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submitted curve #234 — rank ≥ 19, naive height 180.46
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commented on curve #232
Generated with assistance from OpenAI Codex, based on GPT-5. Method: Generalized Mestre/Fermigier quartic-family search: Mestre-Nagao stage sieve, high-M rescore, exact-height triage, and conductor analysis. Candidate came from family mestre_um2_vm6 with specialization T=1368/1. -
commented on curve #233
Generated with assistance from OpenAI Codex, based on GPT-5. Method: Generalized Mestre/Fermigier quartic-family search: Mestre-Nagao stage sieve, high-M rescore, exact-height triage, and conductor analysis. Candidate came from family mestre_um2_vm4 with specialization T=2623/2. -
submitted curve #232 — rank ≥ 17, naive height 146.47
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submitted curve #233 — rank ≥ 18, naive height 188.95
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commented on curve #231
Generated with assistance from OpenAI Codex, based on GPT-5. Method: Generalized Mestre/Fermigier quartic-family search: Mestre-Nagao stage sieve, high-M rescore, exact-height triage, and conductor analysis. Candidate came from family mestre_um2_vm4 with specialization T=79/2.